The discrete horospherical $p$-Minkowski problem in hyperbolic space

In \cite{LX}, the first author and the third author introduced and studied the horospherical $p$-Minkowski problem for smooth horospherically convex domains in hyperbolic space. In this paper, we introduce and solve the discrete horospherical $p$-Minkowski problem in hyperbolic space for all $p\in (-\mathrm{\infty },+\mathrm{\infty })$ when the given measure is even on the unit sphere.